That is a good question. In addition to the sky being blue, you may notice also that the sky maybe a orange-yellow early in the morning or a indigo color as the sun it sets in the evening. I am not very sure of all the answers, but one way I can think of sky is that it is a space in which sun rays penetrate. Sun is light, and light is composed of different colours; the basic ones (the rainbow colours) are red, orange, yellow, green, blue, indigo, violet (and a combination of all these). I think that during the day the blue rays of the sun (which are formed from a combination of some of the basic light colours) penetrate the atmosphere, and that is why we think the sky is blue. In the evening, different rays of the sun (the red, orange and indigo) are able to penetrate the atmosphere, hence we see a different colour in the sky, a reflection of the rays of the sun.
@Kings I think it is the sea that is blue… not! :p
Light from the sun can be split up into several colours, like when it rains while still sunny and the rainbow forms – this is called diffraction. Now, because of the composition of the atmosphere during the day, this light is split into the several “colours”, with the most prominent being blue. This is why we see the sky as blue on a clear day.
Funny thing about light is that despite it being made up of all the different colours our eyes are selective to certain colours. We are most sensitive to the colour green for example. For us to see light must be absorbed by atoms and the reemitted and our eyes detect the light. This process of absorption and reemission is called scattering. As for sunlight the short wavelength high frequency colours blue, indigo and violet are more readily scattered by particles in the atmosphere than the long wavelength ones (red, orange). The long wavelength light just pass through. Our eyes preferentially pick up blue hence the blue sky.
If you are interested, a very nice TV show called “Cosmos A Space Time Odyssey”, my personal favourite show currently, has avery nice history of light in episode 5.